Journal of Applied Probability

Stopping probabilities for patterns in Markov chains

Renato Jacob Gava and Danilo Salotti

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Consider a sequence of Markov-dependent trials where each trial produces a letter of a finite alphabet. Given a collection of patterns, we look at this sequence until one of these patterns appears as a run. We show how the method of gambling teams can be employed to compute the probability that a given pattern is the first pattern to occur.

Article information

J. Appl. Probab., Volume 51, Number 1 (2014), 287-292.

First available in Project Euclid: 25 March 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G42: Martingales with discrete parameter

Stopping time waiting time gambling team martingale Markov chain pattern stopping probability


Gava, Renato Jacob; Salotti, Danilo. Stopping probabilities for patterns in Markov chains. J. Appl. Probab. 51 (2014), no. 1, 287--292. doi:10.1239/jap/1395771430.

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